A study of the prior art has revealed two documents which describe processes wherein at least one of the products isolated is but-1-ene, these being patents FR-B-2 527 201 and EP-B-0 129 900. The patent FR-B-2 527 201 describes a process in several steps starting with a charge of hydrocarbons having 4 carbon atoms. After undergoing several treatments including an etherification reaction with an aliphatic alcohol, then several treatments for the separation of the various constituents of the mixture, but-1-ene is recovered in a top fraction of a distillation column, the bottom fraction being composed of the other compounds and of non recovered but-1-ene. Said bottom fraction is then passed to an isomerization zone where it is partly converted to isobutene. The patent EP-B-0 12 900 describes a process for producing but-1-ene by isomerization starting with a mixture of hydrocarbons containing but-2-enes. This document raises an important problem which is the service life of the isomerization catalyst and hence of the regeneration of said catalyst. The type of catalyst used is an acid catalyst and the operating conditions of the reaction require a reaction temperature of the order of 250.degree. C. to 400.degree. C. Moreover, this process generates isobutene which is difficult to separate from but-1-ene, even if this compound is present only in traces.